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Question
Answer the following:
Find composite of f and g:
f = {(1, 1), (2, 4), (3, 4), (4, 3)}
g = {(1, 1), (3, 27), (4, 64)}
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Solution
f = {(1, 1), (2, 4), (3, 4), (4, 3)}
g = {(1, 1), (3, 27), (4, 64)}
∴ f(1) = 1, f(2) = 4, f(3) = 4, f(4) = 3
∴ g(1) = 1, g(3) = 27, g(4) = 64
(g ° f) (x) = g (f(x))
(g ° f) (1) = g (f(1)) = g (1) = 1
(g ° f) (2) = g (f(2)) = g (4) = 64
(g ° f) (3) = g (f(3)) = g (4) = 64
(g ° f) (4) = g (f(4)) = g (3) = 27
∴ g ° f = {(1, 1), (2, 64), (3, 64), (4, 27)}
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